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  • Articles  (1,018)
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  • Mathematics  (1,018)
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  • Oxford University Press  (1,018)
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  • 1
    Publication Date: 2015-06-09
    Description: This article evaluates 186 papers, published between 1978 and 2013 in 16 representative scientific journals, related to maintenance and reliability problems that were tackled from a multi-criteria (MC) perspective. An overview and insights are presented. This study may be useful to researchers and others concerned with maintenance and reliability who seek not only to understand the potential of MC and multi-objective models but also to develop and apply an MC decision model to help solve a real problem in these areas. There are some discussions on some principles for the application of MC in maintenance and reliability and some guidance on how to choose a suitable MC method is given, based on previous applications.
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  • 2
    Publication Date: 2015-06-09
    Description: A credit-linked note (CLN) is a type of credit derivative, constructed with a bond and an embedded credit default swap, which allows the issuer to transfer a specific credit risk to credit investors. In this paper, we model CLNs with and without counterparty risk in the reduced-form framework. For CLNs with counterparty risk, we consider two different scenarios, i.e. the issuer of CLNs and reference assets have either positive correlation or negative correlation. Assuming the interest rate follows the Cox–Ingersoll–Ross (CIR) model (Cox et al ., 1985) and the default events mainly depend on the interest rate, we model the two different correlations. Explicit formulas for value functions are obtained through a partial differential equation approach. In addition, counterparty valuation adjustment and the dependence on related parameters are also investigated.
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  • 3
    Publication Date: 2016-03-27
    Description: This paper investigates a time consistent multiperiod mean–variance (MV) portfolio selection problem under the Markov regime-switching framework. We use a vector auto-regression model to forecast the values of market factors and then predict the returns of risky assets by using a regime-dependent linear multifactor model. By introducing the notion of separable expected conditional mapping, we construct a time consistent multiperiod MV model with regime switching. Under the self-financing constraint, we derive an analytical optimal investment policy satisfying time consistency and the corresponding MV efficient frontier by using dynamic programming. Empirical results are provided to illustrate the reasonability and practicality of the proposed new model and the derived explicit investment strategy. Especially, we find that the investor invests more in risky assets under a bull market than that under a consolidation market or a bear market; the MV efficient frontier under a bull market is much superior to those determined under a consolidation market and a bear market.
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  • 4
    Publication Date: 2016-03-27
    Description: ABC classifications can be constructed based on a wide range of approaches (varying from formal multi-criteria optimization models to more subjective approaches like the analytic hierarchy processes). Several multi-criteria inventory classification (MCIC) models in particular have recently been proposed in the academic literature. However, even in the presence of the same criteria and the same input data, these models may offer considerably different ABC classifications. That is, for example, an item that is classified based on a certain model in the most important class (class A for example) could be classified by another model in the least important class (class C for example). Such discrepancies have motivated the work described in this paper the objective of which is to tackle the inconsistent operation of existing models for ABC classifications. Based on two well-known MCIC models proposed in the literature, we first develop a new hybrid model which succeeds in reducing the conflict in the resulting classifications. We then propose some new procedures that may take as an input differing ABC classifications to reach as an output a consensus between them. The efficiency of such procedures is evaluated through a number of computational experiments performed on a dataset commonly used in the inventory literature. Using such a dataset allows us to contrast our results with those reported by other researchers.
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  • 5
    Publication Date: 2016-03-27
    Description: An M/M/1 retrial queue is studied for local area network applications in which the server will take delayed vacations upon completion of a service. An announced price charged by the server is imposed on the customers who decide to enter the system for service. These customers have to make decisions upon arrival to balk or to enter the system for service based on their expected payoff and available information about the status of the server. On the other hand, the server faces the revenue maximization issue once the customers' Nash equilibrium strategies are obtained for any announced price. We further study how the social planner, whose goal is to maximize the overall welfare of the customers and the server, determines the price to charge a joining customer. Finally, the sensitivity of the solution of revenue optimization and the socially optimal price as well as the balking behaviour of customers with respect to some main indicators of the system are explored via numerical experiments.
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  • 6
    Publication Date: 2016-03-27
    Description: Amateur baseball contests, particularly those involving young players, often feature a run limit, which establishes a maximum number of runs that may be scored in a half-inning of play. Although conventional wisdom can be used for designing the batting order under standard baseball rules, the composition of the optimal lineup under run limit is still unclear, and the best batting order could differ significantly from the traditional ordering. In this paper, we consider the impact of run limits on the design of the optimal batting order, by developing a Markov chain model for calculating the expected number of runs scored (ENRS) under 3- and 5-run limits. We apply this model to both a high-quality and a lower-quality team, using the data from the 2011 Little League World Series, and illustrate the effect of run limit on the ENRS and the optimal batting order.
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  • 7
    Publication Date: 2015-12-16
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  • 8
    Publication Date: 2015-12-16
    Description: The close–open vehicle routing problem (VRP) with time windows is a realistic variant of the classical VRP with customers that must be served in a specific time interval and where some routes are open and others are closed. A typical situation in logistics and transport activities is when many companies opt for collaboration and recruitment of other specialist companies to carry them out. The company has its own fleet of vehicles and hires the services of other companies that provide complementary resources for specific service needs or business strategy. The aim of this paper is to test the variable neighbourhood search algorithm for solving this problem. In this paper, we present some results using different strategies to obtain the neighbourhoods, applying real problem instances and some Solomon instances.
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  • 9
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    Oxford University Press
    Publication Date: 2016-03-27
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  • 10
    Publication Date: 2016-03-27
    Description: This paper presents a new heuristic for fast approximation of VaR (Value-at-Risk) and CVaR (conditional Value-at-Risk) for financial portfolios, where the net worth of a portfolio is a non-linear function of possibly non-Gaussian risk factors. The proposed method is based on mapping non-normal marginal distributions into normal distributions via a probability conserving transformation and then using a quadratic, i.e. Delta–Gamma, approximation for the portfolio value. The method is very general and can deal with a wide range of marginal distributions of risk factors, including non-parametric distributions. Its computational load is comparable with the Delta–Gamma–Normal method based on Fourier inversion. However, unlike the Delta–Gamma–Normal method, the proposed heuristic preserves the tail behaviour of the individual risk factors, which may be seen as a significant advantage. We demonstrate the utility of the new method with comprehensive numerical experiments on simulated as well as real financial data.
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  • 11
    Publication Date: 2016-03-27
    Description: This paper focuses on an optimal management problem for a general insurance company which contains an insurer and a reinsurer. The general company aims to maximize the expected exponential utility of the weighted sum of the insurer's and the reinsurer's terminal wealth. In our model, the basic claim process is assumed to follow a Brownian motion with drift. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset, respectively. The prices of risky assets are described by the constant elasticity of variance (CEV) models. In addition, the insurer can purchase proportional reinsurance from the reinsurer. By solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation, we derive the optimal reinsurance and investment strategies for the insurer and the reinsurer, respectively. Finally, numerical simulations are presented to show the effects of model parameters on the optimal reinsurance and investment strategies.
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  • 12
    Publication Date: 2016-03-27
    Description: This paper deals with the interaction between polluting firms, tax inspectors and politicians in a corrupted context. We construct a theoretical game model with incomplete information to discuss the effects of such interaction on environmental policy. In this respect, we believe that the State may pursue environmental protection by employing two alternative strategies: on the one hand, the State can, through greater incentive for the tax inspector, increase the monitoring level that reduces the evasion and thus increase tax revenues ( incentive channel ); on the other hand, the State can, through greater environmental expenses, increase the compliance of the polluting firm which means lower evasion and, thus greater tax revenues ( compliance channel ). Clearly, more environmental expenses mean, ceteris paribus , less public resources for the tax inspector's incentive, and vice versa. In this context, we demonstrate that, for a country with a high (low) level of incentives, the incentive (compliance) channel is more efficient than the compliance (incentive) channel.
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  • 13
    Publication Date: 2015-12-16
    Description: The inventory routing problem (IRP) deals with the study of the inter-relationship between two important activities in the supply chain: transportation of commodities and inventory management. In this paper, we study a variant of the multi-product IRP and we propose a general variable neighbourhood search metaheuristic for solving it. We present several neighbourhood structures based on the movement of quantities between routes and periods. Computational experiments show the efficiency of the proposed metaheuristic when compared with the state-of-the-art based on variable neighbourhood search.
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  • 14
    Publication Date: 2015-12-16
    Description: Several variants of variable neighbourhood search (VNS) for solving unconstrained and constrained continuous optimization problems have been proposed in the literature. In this paper, we suggest two new variants, one of which uses the recent modified Nelder–Mead (MNM) direct search method as a local search and the other an extension of the MNM method obtained by increasing the size of the simplex each time the search cannot be continued. For these new and some previous VNS variants, extensive computational experiments are performed on standard and large non-differentiable test instances. Some interesting observations regarding comparison of some VNS variants with NM based local search are made.
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  • 15
    Publication Date: 2015-12-16
    Description: In this paper we report the results of an extensive computational study on a variety of rich vehicle routing problems in which two fundamentally different paradigms or strategies of applying (the same set of) different neighbourhoods are assessed with respect to effectivity (solution quality) and efficiency (speed). We especially compare the structured approach known from variable neighbourhood search where neighbourhoods are applied in some fixed sequential order with an approach where neighbourhoods are applied concurrently. Since all approaches are implemented using the same basic modules, differences can be attributed to this strategic difference. We can show that, first, the application of large neighbourhoods is essential for quality, and, second, that the concurrent strategy outperforms the sequential strategy.
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  • 16
    Publication Date: 2015-12-16
    Description: Variable neighbourhood search (VNS) and all its variants have been successfully proved in hard combinatorial optimization problems. However, there are only few works concerning parallel VNS algorithms, compared with the amount of works devoted to sequential VNS design. In this paper, we propose different parallel designs for the VNS schema. We illustrate the performance of these general strategies by parallelizing a new VNS variant called variable formulation search (VFS). Specifically, we propose six different variants which differ in the VNS stages to be parallelized as well as in the communication mechanisms among processes. We group these variants into three different templates. The first one is oriented to parallelize the whole VNS method. The second one parallelizes the shake and the local search procedures. Finally, the third one explores in parallel the set of predefined neighbourhoods. We test the resulting designs on the cutwidth minimization problem (CMP). Experimental results show that the parallel implementation of the VFS outperforms previous methods in the state of the art for the CMP. This fact is also confirmed by non-parametric statistical tests.
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  • 17
    Publication Date: 2015-12-16
    Description: In this paper, we propose a new heuristic for the covering design problem based on a large neighbourhood search (LNS) metaheuristic that can be seen as a special case of a variable neighbourhood search. As the initial solution, we use a well-known greedy heuristic as well as a new tie-braking rule within greedy algorithms for choosing blocks in the covering. Some theoretical aspects of the greedy heuristic are discussed. The proposed LNS-based heuristic called level reduction can be applied to any covering design and different pre-defined orders, such as lex, colex, etc. With our simple approach, we establish 21 new best known upper bounds on the covering number.
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  • 18
    Publication Date: 2016-06-11
    Description: The dual market phenomenon, in which a product's market is segmented into early and main markets, has attracted much attention in the field of innovation diffusion. It is known that main market adopters, also called the majority, begin to enter the market after a certain period, based on their levels of price sensitivity, which differ from those of early market adopters. This paper proposes a new dual market model that explicitly considers the delayed entry of the majority. We empirically estimate the delayed entry time (DET) for various consumer electronic products, comparing them with two other related phenomena of the early stages of diffusion: take-off and saddle. We also examine whether the DET of a new product can be predicted before it is reached. The result shows that the DET is predictable, using the coefficients of external and internal influence of the early market, also using those of the single market estimated from limited early data. The findings are managerially helpful because being aware of DET at an early stage enables managers to make timely decisions for serving the mass market.
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  • 19
    Publication Date: 2016-06-11
    Description: After demonstrating four basic properties a multi-period risk measure should satisfy, a class of generalized convex multi-period risk measures is defined, which improves and extends existing coherent and convex multi-period risk measures. With respect to this kind of generalized convex multi-period risk measure, the equivalence among different notions of time consistency of risk measure is established. Furthermore, by introducing a fair property that any sophisticated multi-period risk measure should satisfy, we show that if the multi-period risk measure is time consistent, then optimal decisions derived under this risk measure also satisfy the time consistency of optimal policy. Finally, we present the concrete structure of the time consistent generalized convex multi-period risk measure, and illustrate through several examples how to construct time consistent generalized convex multi-period risk measures from existing single-period risk measures.
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  • 20
    Publication Date: 2016-06-11
    Description: We consider a finite-horizon differential game with a legal producer and a counterfeiter as players. The planning horizon is divided into two periods. In the first period, the legal producer is alone in the market, while in the second both players compete. Each player controls his own retail price and advertising budget. We characterize the equilibrium pricing and advertising strategies of the two players, and assess the impact of the counterfeiter's entry date on these strategies. Further, by contrasting the results of the scenarios with and without counterfeiting, we determine the conditions under which the presence of the illegal producer is beneficial to consumers and even to the legal firm.
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  • 21
    Publication Date: 2016-06-11
    Description: Organizations need to better design, manage and improve their supply chains as these become global and more complex. To do this, they need to learn from other organizations and sectors, preempt problems before they occur, and understand the future challenges they may face. Although over 40,000 articles and books have been published on supply chain management since the term was coined in 1982, a clear understanding of the emerging trends, current knowledge gaps and potential areas for future development is only now emerging. Our bibliometric analysis of the existing literature suggests we still need to better understand how to manage security, insourcing, sustainability, competition, risk and disruption, and human behaviour within supply chains. Equally, there is still a lack of research within healthcare, disaster and humanitarian supply chains, as well as within small and medium enterprises. supply chain management; research; surveys; bibliometrics.
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  • 22
    Publication Date: 2016-06-11
    Description: This paper extends the Malmquist productivity index by considering an important factor called the ‘balance factor’. Although factors such as efficiency, scale and technology have been considered before, here the effect of imposed strategies on decision-making units (DMUs) is considered. For this purpose, we develop a new model to calculate the balance of DMUs and take into account the effect of this factor in the Malmquist index in addition to three previous factors. The objective of defining the balance factor is to compute to what extent DMUs are aligned with strategies defined by policy-makers. An empirical case study illustrates the need for such a new index and compares the traditional and extended Malmquist index.
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  • 23
    Publication Date: 2016-09-11
    Description: We consider a passive investor who divides his capital between two assets: a risk-free money market instrument and an index fund, or an exchange-traded fund, tracking a broad market index. We model the evolution of the market index by a lognormal diffusion. The agent faces both fixed and proportional transaction costs and solvency constraints. The objective is to maximize the expected utility from the portfolio liquidation at a fixed horizon, but if the portfolio reaches a pre-set target value, then the position in the risky asset is liquidated. The model is formulated as a parabolic impulse control problem and we characterize the value function as the unique constrained viscosity solution of the associated quasi-variational inequality. We show the existence of an impulse policy which is arbitrarily close to the optimal one by reducing the model to a sequence of iterated optimal stopping problems. The value function and the quasi-optimal policy are computed numerically by an iterative finite element discretization technique. We present extended numerical results in the case of a constant relative risk aversion utility function, showing the non-stationary shape of the optimal strategy and how it varies with respect to the model parameters. The numerical experiments reveal that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buy-and-hold trading strategy where the agent recalibrates his portfolio very few times.
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  • 24
    Publication Date: 2016-09-11
    Description: Maritime security assessment is moving towards a proactive risk-based regime. This opens the way for security analysts and managers to explore and exploit flexible and advanced risk modelling and decision-making approaches in maritime transport. In this article, following a review of maritime security risk assessment, a generic quantitative security assessment methodology is developed. Novel mathematical models for security risk analysis and management are outlined and integrated to demonstrate their use in the developed framework. Such approaches may be used to facilitate security risk modelling and decision making in situations where conventional quantitative risk analysis techniques cannot be appropriately applied. Finally, recommendations on further exploitation of advances in risk and uncertainty modelling technology are suggested with respect to maritime security risk quantification and management.
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  • 25
    Publication Date: 2016-09-11
    Description: In this paper, a bivariate semi-Markov reward chain (BVSMC) model is presented. Equations for the higher order moments of the reward process are presented for the first time and applied to the problem of modelling the credit spread evolution of an obligor by considering the dynamic of its own credit rating and that of a dependent obligor called the counterpart. The paper shows how to compute the expected value of the accumulated credit spread (expressed in basis points) that the obligor should expect to pay in addition to the risk free interest rate. Higher order moments of the accumulated credit spread process convey important financial information in terms of variance, skewness and kurtosis of the total basis points the obligor should with pay in a given time horizon. The paper contributes to the literature by extending on previous results on the semi-Markov reward chains, BVSMC and credit spread modelling by providing unifying approach to these problems. The model and the validity of the results are illustrated through a numerical example.
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  • 26
    Publication Date: 2015-06-09
    Description: In this paper, we study competition and coordination issues in a duopoly distribution channel where two boundedly rational agents compete on their retail price and warranty policy. The paper analyses the dynamics of competition for three different possible cases where retailers compete: (i) exclusively on price, (ii) exclusively on warranty duration and (iii) both on price and warranty duration. We show that price and warranty competition are dynamically stable in nature under certain condition(s). In such cases, each competition model converges to an equilibrium. However the speed of the parameter adjustment determines how quickly the dynamic game will reach equilibrium and the paper analyses the stability of such an equilibrium. The model is illustrated through a numerical study and the results show that though coordination enhances system profit, it may affect the consumers with higher product price and lower warranty duration. Hence, in some cases, competition serves the firms better than coordination, particularly in terms of ‘ social welfare ’.
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  • 27
    Publication Date: 2015-06-09
    Description: Based on empirical analysis of the Capesize and Panamax indices, we propose different continuous-time stochastic processes to model their dynamics. The models go beyond the standard geometric Brownian motion, and incorporate observed effects like heavy-tailed returns, stochastic volatility and memory. In particular, we suggest stochastic dynamics based on exponential Lévy processes with normal inverse Gaussian distributed logarithmic returns. The Barndorff-Nielsen and Shephard stochastic volatility model is shown to capture time-varying volatility in the data. Finally, continuous-time autoregressive processes provide a class of models sufficiently rich to incorporate short-term persistence of freight rates. Our proposed dynamical models are fitted to market data. Finally, a numerical Value-at-Risk exercise is provided that illustrate the significance of using more sophisticated models than geometric Brownian motion.
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  • 28
    facet.materialart.
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    Oxford University Press
    Publication Date: 2015-06-09
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  • 29
    Publication Date: 2014-12-05
    Description: An improved Weiszfeld algorithm, termed the fortified Weiszfeld algorithm, for the solution of the single facility Weber problem with Euclidean distances is proposed. The new approach is based on a parabolic approximation of the objective function and testing demand points for optimality. Computational experiments show the superiority of the fortified approach to the original Weiszfeld algorithm.
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  • 30
    Publication Date: 2014-12-05
    Description: This paper presents a semi-parametric method for bootstrapping non-stochastic estimates of Malmquist indices and the second-stage regressions with a coherent data-generating process (DGP) for panel data. It emphasizes the importance of using censoring techniques instead of truncation in the DGP. To keep the panel structure, the fixed effects censored least square (CLS) method is preferred in the algorithm. Two smoothing processes in the DGP using fixed effects CLSs and cross-sectional censored least absolute deviations are proposed and compared. This semi-parametric bootstrap process can be used to delete artificial correlation amongst the estimated efficiencies in panel data. Although the exposition gives only output-oriented indices, the method can easily be extended to the input-oriented model. Finally, an empirical case study is carried out on Irish dairy farms.
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  • 31
    Publication Date: 2014-12-05
    Description: Conventional data envelopment analysis models have been introduced for technologies only with non-negative inputs and outputs. But in real-world applications, we have some outputs and/or inputs which can take negative values. Especially, in some cases both positive and negative data appear simultaneously in output/input data. In this paper, we review and compare the most recent approaches introduced in the literature. Then, with recourse to some numerical examples, we show that present approaches may fail under two main categories in performance analysis: (a) in introducing non-negative efficient targets in the Pareto sense and (b) in introducing a complete efficiency score for the units. Subsequently, we propose a two-phase slack-based measure model which tackles both problems in an aggregated model. An empirical application in banking is used to illustrate the approach.
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  • 32
    Publication Date: 2014-12-05
    Description: Operating theatre scheduling is a critical task that directly impacts the efficient delivery of surgical care. In this context, we propose a comprehensive stochastic programming modelling framework which handles the inherent uncertainty characterizing the arrival of emergency patients and the duration of surgery. In particular, three recourse strategies are presented with the aim of modelling different reactive scheduling policies actually adopted by hospital managers. In order to solve realistic-sized instances in a reasonable amount of time, we develop tailored heuristic solution strategies that exploit the problem structure. Computational results obtained on a set of randomly generated problems show the effective impact of the stochastic programming approach and the efficiency of the proposed heuristics.
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  • 33
    Publication Date: 2012-03-13
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  • 34
    Publication Date: 2012-12-15
    Description: One of the key drivers of seasonal behaviour in time series is weather, most notably temperature. Very often weather effects are inter-correlated with the impact of other one-off events like public holidays or promotional activity. Due to the uncertainty that comes with short-term weather forecasts, the exact effect of weather on weekly or daily sales has been given very little attention in the forecasting literature. The present study evaluates the impact of weather-driven adjustments to forecasts in a Brewing company. The forecasting team applies a decomposition approach, where: (a) an exponentially smoothing model is used in order to produce weekly sales forecasts; (b) an econometric model is built once a year in order to estimate the impact of 10-day ahead temperature changes in sales (as an input to this model, weekly weather forecasts from the Met office are used); (c) the sales forecasts from the former are adjusted based on the impacts from the latter, as well as for promotions, one-off events and regular seasonal behaviour. Empirical findings suggest that the weather adjustment mechanism improves the forecasting function in the company.
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  • 35
    Publication Date: 2012-12-15
    Description: This paper addresses the capital budgeting problem under uncertainty. In particular, we propose a multistage stochastic programming model aimed at selecting and managing a project portfolio. The dynamic uncertain evolution of each project value is modelled by a scenario tree over the planning horizon. The model allows the decision maker to revise decisions by decommitting from a given project if it shows a negative performance. Risk is explicitly assessed by defining a mean-risk objective function, where the conditional value at risk is used. A customized branch-and-bound method is also introduced for solving the proposed model. Extensive computational experiments have been carried out to validate the model effectiveness, also in comparison with other possible benchmark policies. The numerical results collected by solving randomly generated instances with the proposed branch-and-bound approach seems to be encouraging.
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  • 36
    Publication Date: 2012-09-18
    Description: Internet Service Providers (ISPs) have the ability to route their traffic over different network providers. This study investigates the optimal routing strategy under multihoming in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the th highest volume of traffic shipped). We call this problem the Top-percentile Traffic Routing Problem (TpTRP). The TpTRP is a multistage stochastic optimization problem. Routing decision for every time period should be made before knowing the amount of traffic that is to be sent. The stochastic nature of the problem forms the critical difficulty of this study. Solution approaches based on Stochastic Integer Programming or Stochastic Dynamic Programming (SDP) suffer from the curse of dimensionality, which restricts their applicability. To overcome this, we suggest to use Approximate Dynamic Programming, which exploits the structure of the problem to construct continuous approximations of the value functions in SDP. Thus, the curse of dimensionality is largely avoided.
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  • 37
    Publication Date: 2012-09-18
    Description: In this paper, we describe a non-linear programming model for operational planning of oil refineries, considering exogenous (external) and endogenous (internal) uncertainties. Three mathematical models based on stochastic programming (two-stage stochastic model) and robust programming (min–max regret model and max–min model) are developed to address these uncertainties. The main purpose of this paper is to address the impact of uncertainty on the operational planning of oil refineries by using different risk profiles. The stochastic approach corresponds to a risk-neutral attitude and optimizes the expected value of the objective function. The robust approach, on the other hand, corresponds to a risk-averse attitude and hedges the decision-maker against the worst values of all possible scenarios, although it does not require the estimation of scenario probabilities. A study based on real data from a Brazilian refinery demonstrates the performance of various approaches. After analysing the oil purchase decisions, we identify a clear relationship between the adopted risk attitude and the quantity and quality of the purchased oil. We also show the strong influence of the product specification constraints on the model decisions.
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  • 38
    Publication Date: 2012-09-18
    Description: We consider the problem of mode estimation in a random design regression model. Confidence sets for the modes can be derived as suitable neighbourhoods for maximum points of a regression estimator. For each sample size n, the neighbourhoods are chosen in such a way that they cover the true modes at least with a prescribed probability. The approach relies on concentration-of-measure inequalities for the regression estimators. The aim of the paper is to derive appropriate assertions for the Nadaraya–Watson estimator and to show how these results can be used for the derivation of universal confidence sets.
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  • 39
    Publication Date: 2012-09-18
    Description: Maximum-loss (Max-loss) was recently introduced as a valuation functional in the context of systematic stress testing. The basic idea is to value a (financial) random variable by its worst case expectation, where the most unfavourable probability measure—the ‘worst case distribution’—lies within a given Kullback–Leibler radius around a previously estimated distribution. The article gives an overview of the properties of this measure and analyses relations to other risk and acceptability measures and to the well-known Esscher pricing principle, used in insurance mathematics and option pricing. The main part of the article focuses then on optimal decision-making—in particular related to portfolio optimization—with Max-loss as the objective function to be minimized. A simple algorithm for dealing with the resulting saddle point problem is introduced and analysed.
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  • 40
    Publication Date: 2012-09-18
    Description: The 2008 credit crisis has deeply affected the price of corporate liabilities in both equity and fixed income secondary markets leading to unprecedented portfolio losses by financial investors. A coordinated intervention by monetary institutions limited the systemic consequences of the crisis, without, however, avoiding a significant fall of corporate bond prices across international markets. In this article, we analyse alternative portfolio optimization approaches in the fixed income market over the 2008–2009 period, a time in which credit derivative markets became very illiquid. All policies are analysed relying on a unique set of market and credit scenarios generated by common and idiosyncratic risk factors on an extended investment universe. The crisis provides an interesting test period to analyse in particular the potential of dynamic versus static portfolio selection approaches. We also consider dynamic portfolio strategies based on multistage stochastic programming versus policy rule-based methods and analyse their relative performance against a corporate bond index widely adopted in practice as a market benchmark.
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  • 41
    Publication Date: 2012-09-18
    Description: Increasing financial pressure on State-controlled pension systems has caused, over the last two decades or so, an unprecedented effort by private pension funds (PFs) and insurance companies to issue new types of retirement vehicles. This article investigates the effects of such widespread phenomenon from the perspective of individual asset–liability management. A multistage stochastic programming problem has been formulated with investment opportunities including PFs, unit-linked contracts and variable life annuities. The introduction of a specific risk measure with respect to a desirable retirement income stream and a planning horizon spanning the entire individuals' working life helps to analyse the implications of observed market dynamics on retirement strategies. We present comparative results focusing on the retirement planning problem for three representative individuals carrying different time horizons but common retirement goals. The results show the benefits over traditional pension accumulation plans of dynamic strategies based on mixed portfolios of retirement products.
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  • 42
    Publication Date: 2012-06-16
    Description: In this paper, we discuss the use of some representation results for double martingales to value and hedge contingent claims in a Markovian regime-switching market. A set of N Markov jump assets is introduced to complete the Markovian regime-switching market. Using a representation for double martingales, we justify the completeness of the enlarged market. An equivalent martingale measure, or price kernel, in the enlarged market is then identified by a measure change. The option pricing formula and the hedging portfolio in the enlarged market is also discussed.
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  • 43
    Publication Date: 2012-06-16
    Description: We present a method for exact computation of the expected value of a non-separable, piecewise linear function of two variables. We assume a stochastic model of two random variables obtained by linear combination of two independent principal components having gamma distributions with integer shape parameters. The method can be implemented so the computational effort is proportional to the number of piecewise affine pieces times the product of the shape parameters of the gamma distributions. It can be used for fast computation of expected values in stochastic dynamic programming.
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  • 44
    Publication Date: 2012-06-16
    Description: The analytic hierarchy process (AHP) is a widely used tool. It is employed in multicriteria decision making and is used to deal with complex problems. Traditionally in the process, decision makers produce a single numerical value indicating their preference between a pair of objectives. As an extension, to encapsulate uncertainty, the decision maker is allowed to select parameters (minimum, mode and maximum) from a triangular distribution. This is referred to as the modified AHP. Our paper investigates what precise form the triangular distribution should take and suggests that the current practice is not ideal.
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  • 45
    Publication Date: 2012-06-16
    Description: The extent to which central banks are able to anticipate the effects of monetary policy can be assessed within the framework of the liquidity-preference proposition. An actuarial-based theory of liquidity preference is developed in this paper, which extends the traditional framework by introducing borrowing restrictions. This setting can be applied to describe a broad range of corporate, financial and economic decisions. A major result of the paper is that the interest rate elasticity of the money demand, and hence, the effectiveness of monetary policy, directly depends on the series of nominal output returns. Some states are characterized in particular, when the money demand is perfectly elastic and monetary policy is useless to deal with output fluctuations. An analysis of the historical data of the economy of the USA is additionally provided, which presents empirical evidence showing that the interest rate elasticity can increase in response to economic fluctuations. It is thus concluded that not only the growth and inflation rates should be taken into consideration when implementing monetary policy—as is currently the case in a majority of countries—but also the statistical description of the series of nominal output returns.
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  • 46
    Publication Date: 2012-06-16
    Description: We present a case study of price optimization applied to forecourt retail of motor fuels. The context of the pricing problem is introduced and the technical approach to demand modelling and price optimization is reviewed. We then present a detailed analysis of the results of a trial of price optimization software at a USA fuel retail network. We demonstrate a statistically significant increase in weekly gross profit dollars resulting from the application of price optimization. We show further that this was obtained with greater control of competitive price position and without a statistically significant loss of volume.
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  • 47
    Publication Date: 2011-11-24
    Description: Selecting the best markets from a large number of different markets with varying levels of capability and potential is a complicated and time-consuming task requiring multiple criteria decision-making solution approaches. One of the uses of data envelopment analysis (DEA) is market selection. This paper proposes a new model for selecting the best markets. The proposed model is based on DEA and considers dual-role factors, weight restrictions and imprecise data, simultaneously. This paper is the first study that applies advanced DEA models for selecting markets. The illustrative application addresses applicability of the proposed model.
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  • 48
    Publication Date: 2011-11-24
    Description: Coal-based power plants in India account for about 53% of installed capacity and contribute to more than 60% of electricity generation. Making use of data envelopment analysis and the Malmquist productivity index, this study analyses the productivity change of these plants during the period 2003–2008. The productivity change is further decomposed into technical efficiency change, technological change and scale efficiency change. The impact on productivity of capacity addition and scrapping obsolete power-generating modules is examined. It is found that the sector recorded an average annual total factor productivity (TFP) growth of 1.2% during the period. The plants located in eastern and southern regions have achieved maximum annual growth of 2.2% and 2.0%, respectively. Plants in the central sector achieved maximum growth of 4.2% annually. It is also found that the impact of capacity addition resulted in reduced TFP growth. This study identifies the plants whose productivity changes have been progressive and regressive; such identification can guide suitable managerial intervention to improve productivity.
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  • 49
    Publication Date: 2011-11-24
    Description: By employing data on 337 bank-year observations, the paper examines the impact of consolidation on efficiency and competition in the Malaysian banking sector during 1996–2008. We employ the Panzar-Rosse (P-R) H -statistic method to evaluate the degree of competition, while Data Envelopment Analysis (DEA) is employed to compute the efficiency of individual banks. The empirical findings from the DEA suggest that the Malaysian banking sector has been relatively inefficient in their intermediation function during the post-merger period. On the other hand, we find that the Malaysian banking sector has been relatively more efficient during the post-merger period under the revenue approach. The test of market contestability by using the P-R method seems to reject both monopoly and perfect market competition conditions indicating monopolistic market behaviours among banks operating in the Malaysian banking sector.
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  • 50
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    Oxford University Press
    Publication Date: 2011-11-24
    Description: Integer programming (IP), also known as discrete optimization, is a way of modelling a very wide range of problems involving indivisibilities (e.g. yes/no investment decisions) and non-convexities (e.g. economies of scale and fixed cost allocation). Such problems arise in many areas; these are mentioned in the paper. However, IP demands ingenuity in both building models and in their solution. Much is still not properly understood. This paper investigates the question: ‘Is IP like Linear Programming (LP)? ’ The mathematical and economic properties of IP will be contrasted with LP. It will be suggested that the mathematics and economics of IP are still not properly understood. Many of the results which apply to LP do not apply to IP. It will be asserted that this lack of understanding reveals inadequacies in both the mathematics and economics.
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  • 51
    Publication Date: 2011-11-24
    Description: A model is presented to characterize the equilibrium in markets of short-term loans. First, the cash demand is characterized as the optimal balance maintained to avoid the losses produced by some portfolio with random payoffs. This problem is formulated in actuarial terms in such a way that the optimal balance is expressed as the quantile function of the probability distribution describing the underlying risk (i.e. the value-at-risk). An expression is then obtained for the semi-elasticity of the demand for balances with respect to the interest rate. The effects of credit and investment flows over the equilibrium can be precisely described on these grounds. In the particular case, when the series of price returns of the underlying portfolio is described by a Gaussian probability distribution, episodes of liquidity crises can be corresponded to specific combinations of the risk parameters and the level of the interest rate. Theoretical evidence is thus given of these phenomena.
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  • 52
    Publication Date: 2011-11-24
    Description: A recent publication identified weaknesses with the current handicapping system for disabled Alpine skiing, suggested minor improvements and tentatively proposed an alternative system. This proposal uses shrinkage methods to allow for varying class sizes and race conditions, unlike the existing system that updates historical factors prior to competition. We now recommend a slightly modified form of this proposal for generic application to any sports that involve class handicapping. Our recommendation is based on an investigation into possible uses of this system in a variety of sports, accompanied by extensive analysis of designed experiments and racing data from the 2008 World Cup competition for disabled Alpine skiing. The main disadvantage of this approach is that final scoring times cannot be computed until after all racing is complete and we address this concern by developing interactive result projections that retain the essential excitement of anticipation.
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  • 53
    Publication Date: 2011-11-24
    Description: Analytic solutions exist only for highly idealized simple problems in stochastic storage; while simulation is available for complex problems, it is generally impractically slow. In this paper, a system of partial differential equations (PDEs), based on a novel combination of the techniques used to value options in finance, is developed and shown to efficiently value stochastic storage. The PDE system requires somewhat non-standard (but well-defined) numerical solution methods, which are up to nine orders of magnitude faster than simulation (and yet yields the same results). These faster calculations should permit better analysis of system design and operating procedures (including optimization) for a large set of problems in physical and financial stochastic storage. The motivation for this work is in the management of significant amounts of wind-generated electricity into a power system, in particular by smoothing out random fluctuations in supply.
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  • 54
    Publication Date: 2011-11-24
    Description: The purpose of this paper is to evaluate the performance of a sample of thirteen commercial banks listed on the Athens Exchange by applying a two-step procedure. In the first step, data envelopment analysis (DEA) is used to model performance in two dimensions: profitability efficiency and efficiency in market value generation. In the second step, a tobit model is bootstrapped in order to identify the drivers of performance. The contribution of this paper to the literature is twofold: to improve on the existing methods employing a new variant of DEA profitability approach by using burden as an (undesirable) output variable in modelling profitability efficiency and to better explain (from a computational statistics perspective) DEA efficiency levels inboth dimensions examined by employing a bootstrapped tobit model. Performance inefficiency is uncovered in both dimensions, but the real problem of inefficiency of the sampled banks is the lower level of performance in market value generation, rather than profitability. Results do not point out positive links between profitability efficiency and performance in the stock market. Relatively large banks exhibit better performance on profitability; most of them reached their optimum size scale, whereas they tend to have the worst performance with respect to the stock market. Some smaller banks seem to have some prospects in market value generation, while performance in the stock market can be explained by cost to income ratio.
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  • 55
    Publication Date: 2011-11-24
    Description: A number of problems in economics, finance and insurance rely on determining the sign of the covariance of two transformations of a random variable. The classical Chebyshev's inequality offers a powerful tool for solving the problem, but it assumes that the transformations are monotonic, which is not always the case in applications. For this reason, in the present paper, we establish new results for determining the covariance sign and provide further insights into the area. Unlike many previous works, our method of analysis, which is probabilistic in its nature, does not rely on the classical Höffding's representation of the covariance or on any of its numerous extensions and generalizations. We motivate our research with several problems arising in economics, finance and insurance.
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  • 56
    Publication Date: 2011-11-24
    Description: Statistical models of football (soccer) match outcomes have potential applications to areas such as the development of team rankings and football betting markets. Much of the published work in this context has typically focused on the use of generalized linear models, which are non-dynamic in the sense that the parameters in the model, which often represent the underlying abilities of each team, are assumed to remain constant over time. Dynamic generalized linear models (DGLMs) on the other hand allow the abilities of each team to vary over time. This paper illustrates the application of a DGLM in the context of football match outcome prediction and describes improvements on similar work previously presented by the author, in relation to the estimation of a parameter in the model, referred to as the evolution variance, which is crucial in terms of optimizing the predictive performance of these types of models. Match results data from the Scottish Premier League from 2003/2004 to 2005/2006 are used to show that the DGLM approach provides improved predictive probabilities of future match outcomes compared to the non-dynamic form of the model. DGLMs are also Bayesian in terms of their structure and so a Bayesian approach to parameter estimation is required. This paper therefore illustrates a practical implementation of the DGLM model that can easily be deployed using the freely available software WinBUGS.
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  • 57
    Publication Date: 2011-11-24
    Description: In Brazilian law, there may be nothing as uncontroversial as the idea that courts are slow, inefficient and unable to attend to citizens’ demand. Court inefficiency has been well acknowledged for many decades. Yet, the crucial question "How bad are they? " has never been answered. For many different reasons, almost all legal research carried out in Brazil has been subjective, relying entirely on conventional wisdom and anecdoctal evidence. The purpose of this paper is to try to address the lack of empirical research on the performance of the Brazilian judiciary. We employ data envelopment analysis to measure the efficiency of Brazilian state courts. Results show that relative efficiency varies substantially across the 27 state courts in the country. Moreover, we will also argue that the lack of human and material resources cannot be blamed as the main reason for inefficiency, as it is traditionally believed. Finally, there seems to be some evidence that court efficiency is correlated with the performance of court management. In other words, efficient courts are those that exhibit better management.
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  • 58
    Publication Date: 2011-11-24
    Description: One of the main motivations for participants in high-level sports competitions is setting records. This paper explores the duration of athletic events records since the Modern Olympic Games have been held. Due to the lack of independence between the duration of these records, the use of traditional survival analysis was ruled out and a novel approach for recurrent events was used. No significant differences have been found either between the duration of records of men's and women's events or between individual and team events. There seem to be differences in the duration of records in some specific categories like track and field events. Both the gap between the Olympic record and the contemporaneous world record and the amount that the Olympic record improves increase the risk of the records being broken. The results obtained confirm that the model may reduce the uncertainty about the number of records expected in the next Olympic Games.
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  • 59
    Publication Date: 2011-11-24
    Description: Recently, Konstantaras et al. (2007, Economic ordering policy for an item with imperfect quality subject to the in-house inspection. Int. J. Syst. Sci. , 38 , 473–482) presented an economic order quantity model with imperfect quality subject to in-house inspection. In their study, two options for handling defectives were proposed. The first option considered the defective items to be sold at a lower price and the second considered the defective items to be reworked to an acceptable quality standard to meet demand. Their inventory model is interesting and valuable, but the process for evaluating the expected profit per unit time for the first option can be improved. The main purpose of this paper is to offer an alternative approach for the model, where we apply a renewal reward theorem to calculate the expected profit per unit time and solve the model without derivatives. Numerical examples are provided to show the solution procedure.
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  • 60
    Publication Date: 2011-11-24
    Description: This paper provides a direct estimate of the cost efficiencies of firms in the US solar energy industry. It suggests that the cost efficiency in the industry is associated with the risk-bearing behaviour of firms. Less efficient firms maintain low price-cost margins and high labour–capital ratios in order to compete with their efficient peers. The study then establishes the linkage between cost efficiency and stock returns. It shows that the change in cost efficiency, rather than cost efficiency itself, possesses a stronger explanatory power for stock returns. A buy-and-hold strategy for stock portfolios of different efficiency levels is then analysed. The 3-year returns of the inefficient firm portfolios tend to outperform the efficient firm portfolios. The finding further shows that the improvement in cost efficiency of the inefficient firms is larger than that of the efficient firms. Previous literature has indicated that inefficient firms have higher failure rate, so they are forced to improve cost efficiency.
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  • 61
    Publication Date: 2011-11-24
    Description: In this paper, we compare ratio analysis with the data envelopment analysis approach. It is shown that using ratio analysis implies that a one multidimensional space is projected onto other subspaces many times. As a result, significant distortion of the performance assessment of units takes place. Our theoretical results are validated by computational experiments on the data taken from financial accounts of Russian banks.
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  • 62
    Publication Date: 2011-11-24
    Description: The data envelopment analysis (DEA) is used extensively for estimating the comparative efficiency of operational units that employ similar production processes. Efficiency optimization, however, is not adequate by itself to ensure the successful operation of an enterprise because it is related only to the internal production process of a business unit. Therefore, the unit, to be able to achieve its goals, should take into consideration external factors, such as customer satisfaction, which reflect the quality of the services provided. In this context, the current paper strongly supports the view that synchronous assessment of both efficiency and quality is necessary. Using the quality-adjusted DEA model of Sherman & Zhu (2006a), we develop a quality-driven, efficiency-adjusted DEA model (QE-DEA) which seeks to provide a road map for a high-quality and high-efficiency operation of every service unit of the sample.
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  • 63
    Publication Date: 2011-11-24
    Description: This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to filtering of non-linear time series.
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  • 64
    Publication Date: 2011-11-24
    Description: Existing methods for the prediction of the final scores in football games focus on modelling the numbers of goals scored by the two competitors with parameter estimation of the assumed model usually based on the maximum likelihood approach. Although this approach allows for sufficiently accurate prediction of the final score, it does not account for large or surprising final scores than may deteriorate parameter estimates. This is especially the case in competitions with insufficient number of games compared to the participating teams (e.g. World Cup or Champions League). In this paper, we propose a weighted likelihood approach which allows the modeller to underweight a specific football score if it is felt that the result was not typical and falsifies (in any way) the parameter estimates. The imposed game weights can be defined subjectively or by assuming a model-based structure where the parameters can be estimated by iterative algorithms. The weight structure usually reflects deviations from the assumed model. Hence, scores that have low probability under the assumed model will be underweighted. This procedure may provide robust estimates even if surprising (under the assumed model) scores are observed. Champions League data are used to demonstrate the potential of the proposed approach.
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  • 65
    Publication Date: 2011-11-24
    Description: A statistical model for development of track and field records is presented. The progression of the best results of each year is fitted by a non-linear regression model with non-constant variance. On this basis, the probability of a new record occurrence as well as the distribution of a new record improvement are derived. We also discuss the problems of record prediction and the existence of ultimate records. Our application deals with the men's 100m sprint and the men's long-jump data.
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  • 66
    Publication Date: 2011-11-24
    Description: Bookmakers odds are an easily available source of ‘prospective’ information that is often employed for forecasting the outcome of sports events. In order to investigate the statistical properties of bookmakers odds from a variety of bookmakers for a number of different potential outcomes of a sports event, a class of mixed-effects models is explored, providing information about both consensus and (dis)agreement across bookmakers. In an empirical study of the Union of European Football Associations Champions League, the most prestigious football club competition in Europe, model selection yields a simple and intuitive model with team-specific means for capturing consensus and team-specific standard deviations reflecting agreement across bookmakers. The resulting consensus forecast performs well in practice, exhibiting high correlation with the actual tournament outcome. Furthermore, the agreement across the bookmakers can be shown to be strongly correlated with the predicted consensus and can thus be incorporated in a more parsimonious model for agreement while preserving the same consensus fit.
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  • 67
    Publication Date: 2011-11-24
    Description: Combinatorial auctions allow bidders to bid on individual items or bundles of items. This enables bidders to take advantage of the synergy or complementarity in their valuations of bundles. However, the number of bundles or packages that a bidder could explore may be large making these auctions too complex. Therefore, a combinatorial auction is often run as an iterative auction involving a series of rounds that progressively lead to a final allocation. In each intermediate round, bids are submitted and then provisional winners are determined. A key element in each round is the provision of price feedback to guide bidders in subsequent rounds. This price feedback can focus on packages or on items. Item (also known as linear) pricing feedback schemes have been widely researched for combinatorial auctions on unique items (where packages consist of one or more unique items but not multiple amounts of any item). It has been observed that such item price schemes have performed reasonably well in a wide variety of auction markets. However, they have not yet been thoroughly tested for auctions where the allocation involves multiple units of different items. In this paper, we extend several item pricing designs to the case of multiple unit combinatorial auctions. We identify a set of performance criteria by which an auctioneer could assess the suitability of a design for their particular case. We then numerically compare the algorithms using an agent-based model. Based on the results, we draw some general conclusions about the strengths and limitations of different schemes.
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  • 68
    Publication Date: 2011-11-24
    Description: The key question in research on dismissals of head coaches in sports clubs is not whether they should happen but when they will happen. This paper applies piecewise linear regression to advance our understanding of the timing of head coach dismissals. Essentially, the regression sacrifices degrees of freedom for increased possibilities of interpretation. In the empirical part, we show that badly performing clubs tend to wait for clear evidence before dismissing a head coach. Dutch soccer clubs only dismiss head coaches during the soccer season when a club loses a match it should not have. We also find that once the decision to dismiss the incumbent head coach has been made, clubs quickly tend to appoint a new one, possibly by attracting an interim coach.
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  • 69
    Publication Date: 2014-03-13
    Description: The aim of this paper was to propose a condition-based maintenance policy for a gradually deteriorating system subject to change in the deterioration rate using on-line detection algorithms. The parameters of the deterioration rate after the change is unknown. The main purpose is to estimate these unknown parameters in order to adapt the condition-based maintenance policy and above all to optimize a global cost criterion.
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  • 70
    Publication Date: 2014-03-13
    Description: The article deals with an economic production lot size model in which the manufacturing process shifts from an ‘in-control’ state to an ‘out-of-control’ state after a certain time span which is exponentially distributed. Rapid production may cause such a type of shifting. During the ‘out-of-control’ state, defective items are accumulated and reworked immediately at some cost for maintaining the quality of the product. The demand of the product is assumed to be stochastic. Shortages are allowed and backlogged. Both partial backordering and complete backordering are studied separately and their comparisons are also done. Production cost, holding cost, backlogging cost, lost sale cost, reworked cost and selling price are taken together to construct the integrated expected average profit function, which is maximized to obtain the optimal production rate, optimal lot size and value of optimum expected average profit by using the calculus method. Six numerical examples with their graphical representation are provided to justify the proposed model.
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  • 71
    Publication Date: 2014-03-13
    Description: A new deterministic mathematical model for North American box-office film grosses is presented. The model may be simplified to a set of non-linear ordinary differential equations describing the evolution over time of the film's gross and exhibited sites. The novel feature of this work is the inclusion of geography-based effects to model moviegoer and exhibitor behaviour. Several key regimes are identified, depending on the popularity of the film, as well as how the screens are divided among geographical regions. Analytical results are presented for several relevant cases. Numerical simulations demonstrate close agreement between the model's predictions and actual box-office data.
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  • 72
    Publication Date: 2014-03-13
    Description: This paper is an attempt to gain mathematical insight into the aggregate–disaggregate intermittent demand approach (ADIDA) forecasting framework, by formulating it as a multi-rate signal processing system. After a brief synopsis of the framework's background, an alternative way to perceive ADIDA from a systemic viewpoint is derived by breaking down its managerial steps into fundamental and well-studied components. Mathematical properties stemming from each separate system block are thoroughly explored and their practical effects are then exemplified through simulated paradigms of common time series patterns. Subsequently, theoretical and practical evidence are combined to draw useful conclusions about the framework's performance and make suggestions on its application. Finally, guidelines for further research are proposed.
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  • 73
    Publication Date: 2014-03-13
    Description: We propose a switching regression model for hedge funds to capture the characteristics of trading strategies through time. The coefficients are governed by a discrete-time Markov chain and are able to switch between regimes. The states of the Markov chain represent different states of the economy. Hedge fund indices from main trading strategies and market indices are chosen as regressors. A filtering technique by Elliott (1994, Exact adaptive filters for Markov chains observed in Gaussian noise. Automatica , 30 , 1399–1408) is used to filter out hidden information and optimal parameter estimates are derived through a filter-based Expectation–Maximization algorithm. Our switching regression model is applied to individual hedge fund series from the Hedge Fund Research database.
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  • 74
    Publication Date: 2014-03-13
    Description: A supply chain relationship with a supplier who is stronger than a manufacturer is considered. The manufacturer purchases custom components from the dominant supplier, and then incurs a processing cost before they can sell the product to end customers where the demand for the product is a random variable with a given continuous distribution. For the supplier, there is asymmetric information about the manufacturer's cost structure which is described as a continuous random variable. This paper constructs a principal-agent model in a supplier-led supply chain to maximize the supplier's profits which include the wholesale profits and the transfer payment from the manufacturer. The proposed model is shown to be a dynamic optimization problem. The optimal wholesale price and transfer payment are obtained by solving the optimization problem based on Pontryagin's maximum principle. The optimal contract under symmetric information is also obtained. Some managerial implications are provided for the supplier contract design in a supplier-led environment. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.
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  • 75
    Publication Date: 2012-03-13
    Description: Provider profiling is the process of evaluation of the performance of hospitals, doctors and other medical practitioners in order to increase the quality of medical care. This paper reports statistical analyses carried out on data arising from a regular survey concerning patients admitted with an ST-elevation myocardial infarction diagnosis in one of a number of hospitals in the Milan area. The main aim is to determine process indicators to be used in health-care evaluation. Effective statistical support for clinical and organizational governance is obtained by analysing and modelling data from clinical registries. A grouping structure and a consequent ranking of hospitals is investigated, taking into account the fact that this kind of survey data are intrinsically grouped at first level by where patients are hospitalized. We compare three different techniques for hospital classification based, respectively, on: (a) traditional comparison of survival rates; (b) analysis of variance components in fitted generalized linear mixed effects models; and (c) non-parametric random effects estimation.
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  • 76
    Publication Date: 2012-03-13
    Description: Coxian phase-type distributions are becoming a popular means of representing survival times within a health care environment. They are favoured as they show a distribution as a system of phases and can allow for an easy visual representation of the rateof flow of patients through a system. Difficulties arise, however, in determining the parameter estimates of the Coxian phase-type distribution. This paper examines ways of making the fitting of the Coxian phase-type distribution less cumbersome byoutlining different software packages and algorithms available to perform the fit and assessing their capabilities through a number of performance measures. The performance measures rate each of the methods and help in identifying the more efficient. Conclusions drawn from these performance measures suggest SAS to be the most robust package. It has a high rate of convergence in each of the four example model fits considered, short computational times, detailed output, convergence criteria options, along with a succinct ability to switch between different algorithms.
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  • 77
    Publication Date: 2012-03-13
    Description: Two methods for designing optimal portfolios are proposed. In order to reduce the variation in the asset holdings and hence the eventual proportional transaction costs, the trading strategies of these portfolios are constrained to be of a finite variation. The first method minimizes an upper bound on the discrete-time logarithmic error between a reference portfolio and the one with a constrained trading strategy and thus penalizes the shortfall only. A quadratic penalty on the logarithmic variation of the trading strategy is also included in the objective functional. The second method minimizes a sum of the discrete-time log-quadratic errors between the asset holding values of the constrained portfolio and a certain reference portfolio, which results in tracking the reference portfolio. The optimal trading strategy is obtained in an explicit closed form for both methods. Simulation examples with the log-optimal and the Black–Scholes replicating portfolios as references show smoother trading strategies for the new portfolios and a significant reduction in the eventual proportional transaction cost. The performance of the new portfolios are very close to their references in both cases.
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  • 78
    Publication Date: 2012-03-13
    Description: We use a simple, sociophysical, agent-based model to gain insight into the relationship between the strength of academic research groups and the researchers they contain and to investigate the optimal size of research groups in a number of academic disciplines. The model suggests a linear relationship between group research quality and group quantity up to an upper critical mass. It further suggests that above this size, research quality no longer increases significantly with group quantity due to a tendency for large research groups to fragment. We use the results of the UK's Research Assessment Exercise to establish empirical evidence that, although the best research groups tend to be large, they frequently tend to have characteristics more akin to small and medium groups. This may be interpreted as indicating that the optimal size of research groups is slightly in excess of the upper critical mass. We speculate that a strong degree of cohesiveness lies behind the success of such groups. The principle managerial message coming from this analysis is that emulation of such success involves optimization of the quality and quantity of communication links between research group members.
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  • 79
    Publication Date: 2012-03-13
    Description: It is possible to prolong the life of some paediatric patients awaiting heart transplantation using ‘bridging’ technology, which involves admission to an intensive care environment. It is expected that such bridging reduces deaths on the waiting list and increases the utilization of donor organs. However, bridging offers no guarantee of survival to transplant and can be very burdensome for the families and patients involved. Furthermore, it requires high-level care on a cardiac unit at a large financial and opportunity cost, raising a number of questions concerning its appropriate use. In this work, we explore whether an analytical mathematical model could provide useful insights into the key relationships associated with paediatric cardiac transplant services. We present the framework of an analytical model developed using queuing theory, along with illustrative results based on model parameter estimates derived from retrospective data.
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  • 80
    Publication Date: 2012-03-13
    Description: In this paper, we modify classical structural models such as the Black–Cox model and Merton’s model by indifference pricing. The reason of doing this is because the assets of a firm, which are traditionally regarded as the underlying and used to hedge the credit risk, are usually non-tradeable in the market. We introduce the firm’s stock and a financial index in the market to hedge the credit risk and derive the price of the defaultable corporate bond by indifference valuation. The corresponding pricing formulae for the valuation are obtained by Green’s function approach in a unified way. Finally, the numerical results show that the introduction of the new parameters like the risk aversion of the investor and the correlation between the tradeable and non-tradeable assets may have a positive impact on the short-term credit spread.
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  • 81
    Publication Date: 2011-12-16
    Description: Driven by a range of modern applications that includes telecommunications, e-business and online social interaction, recent ideas in complex networks can be extended to the case of time-varying connectivity. Here, we propose a general framework for modelling and simulating such dynamic networks, and we explain how the long-time behaviour may reveal important information about the mechanisms underlying the evolution.
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  • 82
    Publication Date: 2011-12-16
    Description: In multiprocessor interactive systems, a number of products are prepared using simultaneously working processors, each contributing to the completion of every product. The completion times of products can be expressed in terms of the starting times of individual processors as max-linear functions. It is not difficult to find the starting times once the completion times are given. However, if two such systems work in parallel, it may be necessary to synchronize their work, i.e. to find starting times so that the products are completed at the same time. This task leads to the problem of solving two-sided max-linear systems, a problem of undecided computational complexity. If the solution set is non-trivial, then the task of finding solutions optimal with respect to a certain criterion arises. In this paper, we propose and examine a number of heuristics for solving non-linear programs with two-sided max-linear constraints and compare their performance.
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  • 83
    Publication Date: 2011-12-16
    Description: In this article, we study discrete time mean-reverting market models. We show that certain choices of initial conditions ensure existence of an equivalent martingale measure and absence of arbitrage for any finite time horizon. Further, it is shown that this model still allows some speculative opportunities. These opportunities cannot be expressed in the terms of arbitrage or asymptotic arbitrage. In particular, a gain can be achieved for a wide enough set of expected utilities for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.
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  • 84
    Publication Date: 2011-12-16
    Description: Demand information sharing is used by many organizations to counter the bullwhip effect. A stream of recent papers claims that the upstream member can mathematically infer the demand at the downstream link (downstream demand inference [DDI]) without any formal information sharing mechanism. In this paper, we investigate DDI when non-optimal forecasting methods are employed by supply chains. We show that in the case of a simple moving average forecast, the demand at the downstream link can be inferred. In the case of single exponential smoothing (SES), downstream demand cannot be inferred and thus needs to be shared. Finally, we quantify the value of sharing demand information when SES is employed.
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  • 85
    Publication Date: 2011-12-16
    Description: In this paper, we consider an investment problem where the objective is to maximize the expected utility of terminal real wealth. We demonstrate that, in the market where there exist a risk-free bond, an index bond and a stock, the problem of maximizing the expected utility of real terminal wealth can be transformed into the problem of maximizing the expected utility of nominal terminal wealth. We find that the optimal real and nominal portfolio choices of an investor with constant relative risk aversion preference are the same when the index bond is available for investment.
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  • 86
    Publication Date: 2011-12-16
    Description: In this paper, we study a multistage production–transportation problem for a make-to-order company with outsourcing options at each stage of production. We formulate the problem as a multi-commodity network flow problem with piecewise linear cost structures by assuming the less-than-truckload transportation mode and non-linear production cost structure. We use polymatroid inequalities to strengthen its linear programming relaxation and present a cutting plane approach to tackle it. The computational results show that the strong formulation gives a tight lower bound and the cutting plane approach can solve the problem efficiently.
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  • 87
    Publication Date: 2014-12-05
    Description: In this paper, we discuss control variate methods with applications to Asian and basket options pricing under exponential jump diffusion models for the underlying asset prices. Conditional on geometric means of asset prices, new control variates for arithmetic Asian and basket options are constructed. Numerical results show that the constructed new control variate X NCV is much more efficient than the classical control variate X CCV even in high-dimensional cases when pricing Asian options. For example, the variance reduction ratios by X CCV are no more than 256 for all the cases whereas those by X NCV vary from 14253 to 95873 for low and normal volatilities, and they vary from 6564 to 16296 for high volatility (=0.5), on average over sample sizes 1024, 2048, 4096, 8192, 16384 and 32768. In the case of basket options, the new control variate is still more efficient than the classical control variate. Moreover, our tests also show that the variances of a trivariate control variate are smaller than either bivariate or single variate control variates for the basket options considered.
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  • 88
    Publication Date: 2014-09-09
    Description: Data envelopment analysis (DEA) uses data on multiple inputs and outputs of a set of decision making units to measure their efficiency. However, the classic DEA model does not take non-discretionary factors into consideration. These factors are not controllable, play an important role in production processes, and ignoring them leads to poor estimation of efficiency. This paper proposes a two-stage procedure to handle non-discretionary inputs. To this end, first, a new imaginary environment is created from the existing environments and next, in this new dummy environment, the multiplier form of the DEA model is used. We perform a simulated comparison to show the advantages of the proposed approach. Finally, a real case study of bank branches with two non-discretionary variables is used to demonstrate the applicability of our approach.
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  • 89
    Publication Date: 2014-09-09
    Description: This paper focuses on the design of a distribution network problem in a three-tiered supply chain under uncertainty. The objective is to determine the optimal number, locations and capacities of plants and warehouses to minimize the overall network costs over a variety of economic growth scenarios. For this purpose, a mixed integer linear programming model is extended in a robust optimization framework and then three heuristic approaches based on genetic and memetic algorithms and a mathematical programming approach are used to solve this problem. The effectiveness of the proposed heuristics and the trade-off between model robustness and solution robustness is investigated and directions for further researches are presented.
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  • 90
    Publication Date: 2014-09-09
    Description: In this paper, a recovery inventory system in which a product is remanufactured by the original equipment manufacturer is considered. The remanufacturing process brings used products up to quality standards that are as rigorous as those of new products. The planning horizon is finite and the demand rate is time varying. For satisfying the demand, there are two options: either new items are produced or the used items are repaired back to an ‘as new’ condition, before being sold again. The returned products are a fraction of the demand and they are stored in the recoverable stocking point (recoverable inventory). At the beginning of the planning horizon, the demand is satisfied by new manufacturing lots of unequal size. When the production stops, the demand is satisfied by remanufacturing lots of unequal size (used products are recovered at a fixed rate) and the intervals between multiple production and repair runs are of unequal length and variable. The aim of this study is the determination of these time intervals, which leads to the formulation of a special optimization problem. The solution of this problem enables the determination of the newly produced and remanufactured quantities that minimize the total cost over the planning horizon. Also a simple procedure is proposed which relies on the decoupling of the problem into two sub-problems and determines the optimal time point of switching from a manufacturing activity to a remanufacturing one.
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  • 91
    Publication Date: 2014-09-09
    Description: Random sums play an important role in insurance claim theory and risk models. This paper aims to explore the numerical characteristics of dependent random sums using copulas. We obtain theoretical formulae for the expectation and variance of random sums in the case of a general copula. The expectation is an extension of the Wald equality and can be used to estimate prospective value, while variance provides a theoretical guarantee for measuring the risk premium. As corollaries, the corresponding results for the compound Poisson process and random sums using Farlie–Gumbel–Morgenstern copulas have been obtained. We also conduct stochastic simulation to verify the accuracy of our theoretical results.
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  • 92
    Publication Date: 2014-12-05
    Description: This article develops a novel probabilistic approach to evaluate, through an approximation, a patent-protected R & D project at a fixed date under very general conditions. In a real options framework, we introduce spatial mixed Poisson processes to describe the dynamics of the project value. In such a fashion, the model is able to account for competition among firms and several sources of uncertainty such as time-to-completion of the project, exogenous shocks, input cost uncertainty, technical uncertainty and asymmetric information under different cost structures. The proposed evaluation procedure is of Bayesian type, in that it moves from a specific a-priori information on the phenomenon under scrutiny.
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  • 93
    Publication Date: 2016-03-27
    Description: In this paper, we present a model for supply chain network design (SCND) with anticipation of variable delivered price competition in markets under deterministic and price-dependent demands and with the presence of rivals. The objective is to design a new SC under a capacity constraint in order to maximize the future profit of the SC in competing markets. The structure of the network of the new SC is assumed to be set ‘once and for all’ as a strategic decision; then the price adjustment is possible throughout the course of the competition as a decision at the operation level. In this paper, a new model for oligopolistic competitive SCND is proposed for each of the following two strategies: (1) ‘single product strategy’ and (2) ‘substitutable product strategy’. Finally, we illustrate the model through several numerical examples.
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  • 94
    Publication Date: 2016-03-27
    Description: Assembly jobs with tree-structured precedence constraints in their bill-of-materials structure are a generalized version of traditional jobs involving only line-structured precedence constraints. The assembly job shop scheduling problem deals with assembly jobs, in contrast to job shop scheduling which deals with only traditional jobs. This research explores the ability of different genetic algorithms (GAs) to solve the assembly job shop scheduling problem. The objective is to minimize the makespan (maximum completion time) of a given set of assembly jobs. Random key GAs are proposed which differ using three factors: decoding, schedule justification and individual rearrangement. The three factors have two, seven and two levels, respectively, resulting in 28 different GAs. Specifically, we have conducted a full factorial design of GAs using forward/backward decoding, 0–6 local steps of justification, with/without individual rearrangement. The aim is to test the performance of GAs using different factor settings. As benchmarks, two heuristics have been proposed. Lingo, a software tool for linear and non-linear optimization problems is also used for solution by setting the time limit to 30 min. The experiments have revealed significant effects of the aforesaid three factors on the performance of the GAs.
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  • 95
    Publication Date: 2016-03-27
    Description: A new research issue in the context of production theory is production without explicit inputs. In such systems, input consumption is not important to the decision-maker and the focus is on output production. In the presence of desirable and undesirable outputs, modelling undesirable outputs is an important problem. This paper discusses the problem of weak disposability in the absence of explicit inputs. A linear production technology is constructed axiomatically to handle desirable and undesirable outputs in production systems without explicit inputs. A simple linear formulation of weak disposability in such systems is proposed that enables us to reduce undesirable production outputs.
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  • 96
    Publication Date: 2016-03-27
    Description: We study the problem of staffing university mathematics support services (MSSs) in which students drop in to the service (without appointment) for tutoring support. Our approach seeks to find the minimum sufficient number of tutors (with appropriate specialities) to present by hour and day to cover student demand with tolerable delays. We employ traditional operational research techniques to aid managers and administrators of MSSs to roster their services. The machine interference type queue is adopted to model the number of student queries within a mathematics support session. We define and solve an appropriate integer program to roster the number of tutors needed to run the service efficiently.
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  • 97
    Publication Date: 2016-03-27
    Description: We study a market where there are traders with different levels of information. Insiders observe exclusive, non-public information that affects the volatility of the price process, and the information levels are different even among insiders. By the nature of information, some information processes are continuous, while others are discrete. We study the local risk minimization hedging strategies of the insiders under stochastic volatility models, and compare them with an honest trader's strategy. A numerical example is provided.
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  • 98
    Publication Date: 2013-07-25
    Description: Open pipeline order fulfilment systems have emerged in sectors such as the automotive industry that offer a large number of product variants to the marketplace. In an open pipeline a customer can be fulfilled from anywhere in the system—by a stock product, by a product in the distribution system, by allocating a product in production or a product in the plan, or by supplying a product specially built to order (BTO). Here new results are presented to estimate the performance metrics for open pipeline systems. An exact expression is developed based on a Markov analysis to calculate the BTO proportion for any combination of the key system parameters—pipeline length, the variety level and the initial stock level. Approximation schemes are developed to estimate the pipeline and stock fulfilment proportions, the mean lead time and the mean stock level. The approximation schemes provide accurate estimates for a large range of systems. Specific issues that affect the estimation of performance metrics in low variety, open pipeline systems are discussed. The results presented provide generic insights for open pipeline systems design and management and provide a platform for further work in extending the applicability of open pipeline concepts.
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  • 99
    Publication Date: 2013-07-25
    Description: This paper presents a methodology and a case study where the proportional hazards model is used to determine the reliability and risk of existing repairable systems in a distribution network utility. After introducing different issues relating to conditioning-maintenance management in these companies, we discuss the modelling possibilities to obtain on-line values for system reliability and risk. In this case, we try to model reliability considering the current operating time of the equipment, the number of maintenance interventions and the value of specific monitored parameters. Reliability is then used to calculate equipment risk for a given failure mode during a certain period, and in order to do so, the effect on the network of the failure mode is estimated from historical data. Finally, the paper presents a possible business process to schedule preventive maintenance activities according to previous findings and a case study.
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  • 100
    Publication Date: 2013-07-25
    Description: Mathematical models are often used to describe the sales and adoption patterns of products in the years following their launch and one of the most popular of these models is the Bass model. However, using this model to forecast sales time series for new products is problematical because there is no historic time series data with which to estimate the model's parameters. One possible solution is to fit the model to the sales time series of analogous products that have been launched in an earlier time period and to assume that the parameter values identified for the analogy are applicable to the new product. In this paper, we investigate the effectiveness of this approach by applying four forecasting methods based on analogies (and variants of these methods) to the sales of consumer electronics products marketed in the USA. We found that all the methods tended to lead to forecasts with high absolute percentage errors, which is consistent with other studies of new product sales forecasting. The use of the means of published parameter values for analogies led to higher errors than the parameters we estimated from our own data. When using our own data, averaging the parameter values of multiple analogies rather than relying on a single most-similar, product led to improved accuracy. However, there was little to be gained by using more than five or six analogies.
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